Image noise reduction and/or image resolution improvement

ABSTRACT

A method for improving image quality of image data includes analyzing, for each of a plurality of voxels of image data, a set of entries of a dictionary, wherein an entry represents a mapping between a lower resolution patch of voxels and a corresponding higher resolution patch of voxel or a local neighborhood around a voxel, deriving, for each of the plurality of voxels, a subspace based on the analysis, wherein the subspace is for one of the mapping or the local neighborhood, and restoring target image data based on the subspaces, wherein the target image data is image data with higher image resolution or reduced image noise.

The following generally relates to reducing image noise and/or improvingimage resolution of acquired image data and is described with particularapplication to computed tomography (CT).

A CT scanner generally includes an x-ray tube mounted on a rotatablegantry that rotates around an examination region about a longitudinal orz-axis. The x-ray tube emits radiation that traverses the examinationregion and a subject or object therein. A detector array subtends anangular arc opposite the examination region from the x-ray tube. Thedetector array includes one or more rows of detectors that are alignedwith respect to each other and that extend along the z-axis. Thedetectors detect radiation that traverses the examination region and thesubject or object therein and generate projection data indicativethereof. A reconstructor processes the projection data and generates 3Dimage data.

However, CT scanners emit ionizing radiation, which may increase a riskof cancer. This concern has been exasperated as the number of CT scanshas increased and as use of CT scanning in asymptomatic patients hasbecome more widespread. Dose deposited to the patient can be reduced bydecreasing tube current and/or voltage and/or the number of scans,and/or increasing the pitch, slice thickness and/or slice spacing.However, image noise is inversely proportional to radiation dose, andthus reducing radiation dose not only reduces the dose deposited to thepatient but also increases image noise in the acquired data, which ispropagated to the image data during reconstruction, reducing imagequality (i.e., noisier, less sharp images), which may degrade thediagnostic value of the imaging data.

A goal of image de-noising is to recover the original image from a noisymeasurement through averaging. This averaging may be performed locally:the Gaussian smoothing model, the anisotropic filtering and theneighborhood filtering by the calculus of variations: the TotalVariation minimization or in the frequency domain: the empirical Wienerfilters and wavelet thresholding methods. Non-local means (NL) is animage de-noising process based on non-local averaging of all the pixelsin an image. In particular, the amount of weighting for a pixel is basedon the degree of similarity between a small patch centered around thatpixel and the small patch centered around the pixel being de-noised.

Image resolution has been improved through super-resolution algorithms.Some super-resolution algorithms exceed the diffraction-limit of theimaging systems, while other super-resolution algorithms provide animprovement over the resolution of the detector. Multiple-framesuper-resolution algorithms generally use sub-pixel shifts betweenmultiple low resolution images of the same scene and improve imageresolution by fusing or combining multiple low resolution images into asingle higher resolution image. Learning-based super-resolutionalgorithms additionally incorporate application dependent priors toinfer the unknown high resolution images.

In view of the above, there is an unresolved need for other approachesfor reducing patient dose while preserving image quality and/or forimproving image resolution.

Aspects described herein addresses the above-referenced problems andothers.

In one aspect, a method for improving image quality of image dataincludes analyzing, for each of a plurality of voxels of image data, aset of entries of a dictionary, wherein an entry represents a mappingbetween a lower resolution patch of voxels and a corresponding higherresolution patch of voxel or a local neighborhood around a voxel,deriving, for each of the plurality of voxels, a subspace based on theanalysis, wherein the subspace is for one of the mapping or the localneighborhood, and restoring target image data based on the subspaces,wherein the target image data is image data with higher image resolutionor reduced image noise.

In another aspect, an image data processor includes an analyzer thatanalyzes, for each of a plurality of voxels of image data, a set ofentries of a dictionary, wherein an entry represents a mapping between alower resolution patch of voxels and a corresponding higher resolutionpatch of voxel or a local neighborhood around a voxel and derives, foreach of the plurality of voxels, a subspace based on the analysis,wherein the subspace is for one of the mapping or the localneighborhood; and an image restore that restores target image data basedon the subspaces, wherein the target image data is image data withhigher image resolution or reduced image noise.

In another aspect, a computer readable medium encoded with computerexecutable instruction, which, when executed by a processor, causes theprocessor to: generate image data with higher image resolution orreduced noise based on initial image data and a non-local principlecomponent analysis (PCA).

The invention may take form in various components and arrangements ofcomponents, and in various steps and arrangements of steps. The drawingsare only for purposes of illustrating the preferred embodiments and arenot to be construed as limiting the invention.

FIG. 1 schematically illustrates an example imaging system in connectionwith an image data processor, which is configured to improve imagequality of image data.

FIG. 2 schematically illustrates an example of the image data processor.

FIG. 3 illustrates a method for improving an image quality.

FIG. 4 illustrates a method for improving an image resolution.

FIG. 5 illustrates a method for reducing image noise.

Initially referring to FIG. 1, an imaging system 100 such as a computedtomography (CT) scanner is schematically illustrated.

The imaging system 100 includes a generally stationary gantry 102 and arotating gantry 104. The rotating gantry 104 is rotatably supported bythe stationary gantry 102 and rotates around an examination region 106about a longitudinal or z-axis.

A radiation source 110, such as an x-ray tube, is rotatably supported bythe rotating gantry 104. The radiation source 110 rotates with therotating gantry 104 and emits radiation that traverses the examinationregion 106. A source collimator includes collimation members thatcollimate the radiation to form a generally cone, wedge, fan or othershaped radiation beam.

A sensitive detector array 112 subtends an angular arc opposite theradiation source 110 across the examination region 106. The detectorarray 112 includes a plurality of rows of detectors that extend alongthe z-axis direction. The detector array 112 detects radiationtraversing the examination region 106 and generates projection dataindicative thereof.

A reconstructor 114 reconstructs the projection data and generatesthree-dimensional (3D) volumetric image data indicative thereof. Thereconstructor 114 may employ a conventional 3D filtered-backprojectionreconstruction, a cone beam algorithm, an iterative algorithm and/orother algorithm.

A subject support 118, such as a couch, supports an object or subjectsuch as a human or animal patient in the examination region 106. Thesubject support 118 is configured to move vertically and/or horizontallybefore, during, and/or after a scan to position the subject or object inconnection with the system 100.

A general-purpose computing system or computer serves as an operatorconsole 120. The console 120 includes a human readable output devicesuch as a monitor or display and an input device such as a keyboard,mouse, etc. Software resident on the console 120 allows the operator tointeract with the scanner 100 via a graphical user interface (GUI) orotherwise, e.g., selecting a dose reducing and/or image qualityimproving algorithm, etc.

An image data processor 116 processes image data, reducing noise and/orimproving image resolution of the image data. As described in greaterdetail below, in one instance, the image data processor 116 reducesnoise and/or improves image resolution of the image date utilizingnon-local principle component analysis (PCA) and a learning-based superresolution algorithm. Reducing image noise as such allows for reducingradiation for a scan (and thus the dose deposited to a patient) whilemaintaining image quality. Improving resolution allows for enhancingimage resolution. A combination of noise reduction and improving imageresolution is also contemplated herein.

The image data processor 116 can be implemented via a processorexecuting one or more computer readable instructions encoded or embeddedon computer readable storage medium such as physical memory or othernon-transitory medium. Such a processor can be part of the console 120and/or other computing device such as a dedicated visualizationcomputer, and/or other computing device. Additionally or alternatively,the processor can execute at least one computer readable instructionscarried by a carrier wave, a signal, or other non-computer readablestorage medium such as a transitory medium.

A data repository 122 can be used to store the image data generated bythe system 100 and/or the image data processor 116, image data used bythe image data processor 116, and/or other data. The data repository 122may include one or more of a picture archiving and communication system(PACS), a radiology information system (RIS), a hospital informationsystem (HIS), an electronic medical record (EMR) database, a sever, acomputer, and/or other data repository. The data repository 122 can belocal to the system 100 or remote from the system 100.

FIG. 2 schematically illustrates an example of the image data processor116.

The illustrated image data processor 116 receives image data to beprocessed to increase resolution and generate higher resolution imagedata. This image data may be lower dose image data being processed toreduce noise and/or improve resolution, for example, to a level of thatof conventional dose image data (or lower or higher). Alternatively, theimage data may be conventional dose image data being processed solely toincrease the resolution. The image data can come from the reconstructor114 (FIG. 1), the data repository 122 (FIG. 1) and/or other device.

A dictionary bank 204 stores various dictionaries. The illustrateddictionary bank 204 includes at least one of a prior generateddictionary 206, a self-similarity dictionary 208 and/or deriveddictionary 210. Each dictionary includes a dictionary for each voxel tobe processed in the image data.

The prior generated dictionary 206 includes an already generateddictionary provided to the image data processor 116.

A dictionary determiner 212 determines the self-similarity dictionary208 and/or derived dictionary 210. The dictionary determiner 212 mayhave determined the prior generated dictionary 206, for example, duringearlier processing of first image data and/or other image datacorresponding to the same patient and/or another patient.

For the self-similarity dictionary 208, the dictionary determiner 212downscales the image data and generates a collection of matches betweenvoxel neighborhoods of the downed scaled image data and the image data.In another embodiment, other voxels may additionally or alternatively becollected. In the context of noise removal, this dictionary is createdas a collection of all the patches in the input study.

For the derived dictionary 210, the dictionary determiner 212 identifiesa voxel neighborhood in a higher resolution image that corresponds to avoxel in the image data using a registration, matching and/or otheralgorithm. The derived dictionary 210 is then derived as a collection ofmatches between the voxel neighborhoods of higher resolution image dataand downscaled higher resolution image data. The down scaling can beachieved by smoothing and/or other processing with an appropriate filterand, optionally, sub-sampling the filtered higher resolution image data.

An optional (high pass) filter 214 filters lower-frequency components inthe dictionary so that a dictionary entry does not have to be stored forall possible lowest frequency component values, i.e., rather thanderiving the dictionary directly on study patches, pre-processinghigh-pass filter is employed, in order to extract local features thatcorrespond to their high-frequency content. The filtering allows forfocusing the training on characterizing the relation between thelow-resolution patches and the edges and texture content within thecorresponding high-resolution ones.

A non-local analyzer 216 obtains, for each voxel, a set of dictionaryentries. The non-local analyzer 216 analyzes this set of entries andderives a subspace for the estimated patch. In the context of noiseremoval, the subspace is for the local neighborhood around the voxel,while in the context of super resolution the subspace is of the mappingbetween low resolution and high resolution patch. More specifically, fornoise removal, for each voxel in the image data, patches that aresimilar to the currently processed patch around the voxel areidentified. A data matrix is then created by putting the patches in thematrix, where each patch is corresponding to a row in the matrix. Anon-weighted or weighted-PCA is then applied to the matrix, where thesamples are the rows of the matrix and, in the case of weighted-PCA, theweights are function of a similarity function between the patch and/orthe local noise level within the patches.

The non-local analyzer 216 then estimates the number of principlecomponents with the largest corresponding eigenvalues which are used tomodel the local signalpatch. Suitable methods for modeling the localsignalpatch include, but are not limited to, Akaike informationcriterion, Bayesian information criterion, deviance informationcriterion, stepwise regression, cross-validation, Mallows' Cp, focusedinformation criterion, thresholding of ratio difference betweenconsecutive eigenvalues and/or other estimation technique.

For super resolution, the steps are similar with the followingexceptions. For each voxel in the input image, dictionary entries with alower resolution patch similar to the currently processed patch aroundthe voxel are identified. Each row in the matrix consists of the wholedictionary entry, i.e., concatenation of two vectors that consist of thelow resolution and high resolution patches of the dictionary entry. Thesimilarity function is between the currently processed patch and thelower resolution patch entry of the dictionary. The estimation of thenumber of principle components is applied, and there are correspondingmeasurements only for the low resolution entry patch of the dictionary.

An optional constraint enforcer 218 enforces one or more predeterminedconstraints, for example, a constraint on identifying similar patches.Such a constraint may be that the number of similar patches with aweighted average value larger than the weighted average value of thecurrently processed patch is equal to the number of patches with asmaller weighted average. This optional constraint can facilitate insome scenarios the preservation of low contrast regions.

An image restorer 220 restores target image data. In the context ofnoise removal, the target image data is a reduced noise image data, andin the context of super resolution the target image data is a higherresolution image data. Suitable restorations include, but are notlimited to, a local approach, a global approach, and/or other approach.

The following describes an example local approach, which utilizes agreedy or other optimization approach. For noise removal, for each voxelin the noisy study, a least-squared is used to solve the optimizationshown in EQUATION 1:

$\begin{matrix}{{\hat{\alpha} = {\underset{\alpha}{\arg \; \min}\left( {P - V_{avg} - {\sum\limits_{i = 1}^{m}{V_{i}\alpha_{i}}}} \right)^{2}K}},} & {{EQUATION}\mspace{14mu} 1}\end{matrix}$

where P is a vector corresponding to the patch around the currentlyprocessed voxel, V_(avg) is vector of mean values of each columns of thematrix A, which includes relevant patches, where each patch correspondsto a row in the matrix, V_(i) is the principle component with the i-thlargest corresponding eigenvalue of the samples in the matrix A, K is aweight kernel that penalizes distance away from the currently processedvoxel and m is the number of principle components that models thecurrently local patch. The recovered noiseless patch is shown inEQUATION 2:

$\begin{matrix}{\hat{P} = {V_{avg} + {\sum\limits_{i = 1}^{m}{V_{i}{{\hat{\alpha}}_{i}.}}}}} & {{EQUATION}\mspace{14mu} 2}\end{matrix}$

The recovered noiseless patches are merged by weighted averaging in theoverlap area to create the final restored image.

For super resolution, for each voxel in the noisy study, a least-squaredis used to solve the optimization shown in EQUATION 3:

$\begin{matrix}{{\hat{\alpha} = {\underset{\alpha}{\arg \; \min}\left( {P - V_{avg}^{lr} - {\sum\limits_{i = 1}^{m}{V_{i}^{lr}\alpha_{i}}}} \right)^{2}K}},} & {{EQUATION}\mspace{14mu} 3}\end{matrix}$

where the lr superscript refers to the vector section that iscorresponding to low resolution patch of the dictionary entry. Therecovered noiseless patch is shown in EQUATION 4:

$\begin{matrix}{{\hat{P} = {V_{avg}^{hr} + {\sum\limits_{i = 1}^{m}{V_{i}^{hr}{\hat{\alpha}}_{i}}}}},} & {{EQUATION}\mspace{14mu} 4}\end{matrix}$

where the hr superscript refers to the vector section that iscorresponding to high resolution patch of the dictionary entry.

The recovered high resolution patches are merged by weighted averagingin the overlap area to create the restored image. In case of usingfiltered patches, the restored image is added to an interpolated studyof the input study.

An additional optional step is to enforce a global restorationconstraint between the low resolution input study and the algorithm'soutput high resolution study. This is done efficiently using aback-projection method as shown in EQUATION 5:

I _(t+1) ^(high) =I _(t) ^(high) +US(I ^(low) −DS(I _(t) ^(high))),  EQUATION 5:

where I^(low) is the input study, I₀ ^(high) is the output study of theprevious step, US is an up-scaling operator and DS is a down-scalingoperator.

An additional optional step is to include a gain parameter with EQUATION5 as shown in EQUATION 6:

I _(t+1) ^(high) =US(I ^(low))+(I _(t) ^(high) −US(I ^(low)))* g  EQUATION 6:

where g is a gain parameter that controls an intensity of the highfrequencies that are added to the image. In one instance, a defaultvalue of g is one (1), and the value of g is be set by presettingdefinition. An alternative option is that the value of g can becontrolled by the user in real time using a scroller or the like, withthe updated result presented in real time on the display.

The following describes an example global approach, which utilizes theoptimization of a global cost function or other function.

For noise removal, all the voxels in the noisy study are simultaneouslyoptimized, for example, using a least-squared is used to solve theoptimization shown in EQUATION 7:

$\begin{matrix}{{{\hat{\alpha}}_{i}^{j} = {{\underset{\alpha_{i}^{j}}{\arg \; \min}{\sum\limits_{j}^{\;}{\left( {P^{j} - V_{avg}^{j} - {\sum\limits_{i = 1}^{m^{j}}{V_{i}^{j}\alpha_{i}^{j}}}} \right)^{2}K}}} + {\lambda {\sum\limits_{j_{1},j_{2},k_{1},k_{2}}^{\;}{\left( {{\hat{P}}_{k_{1}}^{j_{1}} - {\hat{P}}_{k_{2}}^{j_{2}}} \right)^{2}K_{k_{1}}K_{k\; 2}I_{{k\; 1},{k\; 2}}^{{j\; 1},{j\; 2}}}}}}},} & {{EQUATION}\mspace{14mu} 7}\end{matrix}$

where P^(j) is a vector corresponding to the patch around the voxel j,{circumflex over (P)}_(k) ^(k) is voxel k in the recovered patch aroundthe voxel j, where the recovered patch around voxel j is

${\hat{P^{j}} = {V_{avg}^{j} + {\sum\limits_{i = 1}^{m^{j}}{V_{i}^{j}{\hat{\alpha}}_{i}^{j}}}}},$

V_(avg) ^(j) is a vector of mean values of each columns of the matrix Afor voxel j, V_(i) ^(j) is the principle component with the i-th largestcorresponding eigenvalue of the samples in matrix A for voxel j, K is aweight kernel that penalizes distance away from its center, m′ is thenumber of principle components that models the patch around voxel j,K_(k) is the k element in the kernel, I_(k1,k2) ^(j1,j2) is an indexthat equal to one only if the k1 element of the patch around voxel j1 isoverlapping in the study with the k2 element of the patch around voxelj2 and λ is a scalar input parameter.

The recovered noiseless patch is shown in EQUATION 8:

$\begin{matrix}{\hat{P^{j}} = {V_{avg}^{j} + {\sum\limits_{i = 1}^{m_{j}}{V_{i}^{j}{{\hat{\alpha}}_{i}^{j}.}}}}} & {{EQUATION}\mspace{14mu} 8}\end{matrix}$

The recovered noiseless patches are merged by weighted averaging in theoverlap area to create the final restored image.

For super resolution, all the voxels in the noisy study aresimultaneously optimized, for example, using a least-squared is used tosolve the optimization shown in EQUATION 9:

$\begin{matrix}{{{\hat{\alpha}}_{i}^{j} = {{\underset{\alpha_{i}^{j}}{\arg \; \min}{\sum\limits_{j}^{\;}{\left( {P^{j} - V_{avg}^{{lr},j} - {\sum\limits_{i = 1}^{m_{j}}{V_{i}^{{lr},j}\alpha_{i}^{j}}}} \right)^{2}K}}} + {\lambda {\sum\limits_{j_{1},j_{2},k_{1},k_{2}}^{\;}{\left( {{\hat{P}}_{k_{1}}^{j_{1}} - {\hat{P}}_{k_{2}}^{j_{2}}} \right)^{2}K_{k_{1}}K_{k\; 2}I_{{k\; 1},{k\; 2}}^{{j\; 1},{j\; 2}}}}}}},} & {{EQUATION}\mspace{14mu} 9}\end{matrix}$

where the lr superscript is referring to the vector section that iscorresponding to low resolution patch of the dictionary entry. Therecovered noiseless patch is shown in EQUATION 10:

$\begin{matrix}{\hat{P^{j}} = {V_{avg}^{{hr},j} + {\sum\limits_{i = 1}^{m_{j}}{V_{i}^{{hr},j}{\hat{\alpha}}_{i}^{j}}}}} & {{EQUATION}\mspace{14mu} 10}\end{matrix}$

where the hr superscript is referring to the vector section that iscorresponding to high resolution patch of the dictionary entry.

The recovered high resolution patches are merged by weighted averagingin the overlap area to create the restored image. In case of usingfiltered patches, the restored image is added to an interpolated studyof the input study.

An additional optional step is to enforce a global restorationconstraint between the low resolution input study and the algorithm'soutput high resolution study. This is done efficiently using aback-projection method as shown in EQUATION 5 above.

FIGS. 3, 4 and 5 respectively illustrate methods for improving imagequality, improving image resolution and reducing noise.

It is to be appreciated that the ordering of the acts in the methodsdescribed herein is not limiting. As such, other orderings arecontemplated herein. In addition, one or more acts may be omitted and/orone or more additional acts may be included.

FIG. 3 illustrates a method for improving image quality.

At 302, a tailored dictionary for each voxel to be processed isobtained. In the context of super resolution, each dictionary entryrepresents a mapping between low resolution and high resolution voxels.In the context of noise removal, a dictionary entry represents abuilding block. As described herein, the tailored dictionary is acombination of prior, self-similarity and/or derived dictionaries.

At 304, for each voxel, a subspace is determined based on an analysis ofa set of corresponding dictionary entries. In the context of superresolution, the subspace is a mapping between lower resolution andhigher resolution voxels. In the context of noise removal, the subspaceis for the local neighborhood around the voxel.

At 306, image data is restored by incorporating local and globalfidelities and compatibilities constraints. In the context of noiseremoval, the target image data is a reduced noise image data, and in thecontext of super resolution the target image data is a higher resolutionimage data. Suitable constraints may include compatibilities ofestimated local signal with its derived signal subspace, compatibilitiesbetween neighbor signal subspaces, compatibility between low resolutionand its estimated high resolution image.

FIG. 4 illustrates a method for improving image resolution.

At 402, a tailored dictionary for each voxel in image data to process isobtained. As discussed herein, each dictionary entry represents amapping between lower resolution voxels and corresponding higherresolution voxels.

At 404, dictionary entries from the tailored dictionary are obtained fora lower resolution patch corresponding to a patch around a voxel toprocess.

At 406, a matrix is created based on the obtained patches. As discussedherein, each row in the matrix consists of the whole dictionary entry,i.e., concatenation of two vectors that consist of the lower resolutionand the higher resolution patches of the dictionary entry.

At 408, a PCA or weighted-PCA is performed on the matrix. For this, thesamples are the rows of the matrix and, in the case of a weighted-PCA,the weights are function of a similarity function between the currentlyprocessed patch and the lower resolution patch entry of the dictionary.

At 410, the number of principle components is estimated. In this case,corresponding measurements are only for the lower resolution entry patchof the dictionary.

At 412, a higher resolution image is restored based on the lowerresolution patches of the dictionary, the matrix, the principalcomponents, the number of principal components, and a local or globaloptimization, as described herein.

FIG. 5 illustrates a method for reducing image noise.

At 502, a tailored dictionary for each voxel in image data to process isobtained. As discussed herein, each dictionary entry represents abuilding block.

At 504, patches that are similar to the currently processed patch arounda voxel are identified.

At 506, a matrix is created based on the obtained patches. As discussedherein, each patch corresponds to a row in the matrix.

At 508, a PCA or weighted-PCA is performed on the matrix. For this, thesamples are the rows of the matrix and, in the case of a weighted-PCA,the weights are function of a similarity function between the patchand/or the local noise level within the patches.

At 510, the number of principle components is estimated. In this case,corresponding measurements are only for the lower resolution entry patchof the dictionary.

At 512, a reduced noise image is restored based on the patches aroundthe voxels, the matrix, the principal components, the number ofprincipal components, and a local or global optimization, as describedherein.

The methods described herein may be implemented via one or moreprocessors executing one or more computer readable instructions encodedor embodied on computer readable storage medium such as physical memorywhich causes the one or more processors to carry out the various actsand/or other functions and/or acts. Additionally or alternatively, theone or more processors can execute instructions carried by transitorymedium such as a signal or carrier wave.

The invention has been described with reference to the preferredembodiments. Modifications and alterations may occur to others uponreading and understanding the preceding detailed description. It isintended that the invention be constructed as including all suchmodifications and alterations insofar as they come within the scope ofthe appended claims or the equivalents thereof.

1. A method for improving image quality of image data, comprising: analyzing, for each of a plurality of voxels of image data, a set of entries of a dictionary, wherein an entry represents either a mapping between a lower resolution patch of voxels and a corresponding higher resolution patch of voxel, or a local neighborhood around a voxel; deriving, for each of the plurality of voxels, a subspace based on the analysis, wherein the subspace is for one of the mapping or the local neighborhood; and restoring the image data to produce the target image data, which has higher image resolution or reduced lungs noise relative to the image data, based on the subspaces, using least-squares to optimize a local or global optimization.
 2. The method of claim 1, wherein deriving the subspace comprises: identifying patches for each voxel in the image data that are similar to a currently processed patch around the voxel; creating a data matrix with the identified patches; performing a PCA to the matrix; and estimating a number of principle components with a largest corresponding eigenvalues to model the local patch.
 3. The method of claim 2, wherein the PCA is a weighted-PCA, wherein weights are a function of either a similarity function between at least one of the patch, or a local noise level within the patches.
 4. The method of claim 2, wherein the local patch is modeled using one or more of: Akaike information criterion, Bayesian information criterion, deviance information criterion, stepwise regression, cross-validation, Mallows' Cp, focused information criterion, or thresholding of ratio difference between consecutive eigenvalues.
 5. The method of claim 1, wherein a number of similar patches with a weighted average value larger than a weighted average value of a currently processed patch is equal to a number of patches with a smaller weighted average.
 6. The method of claim 1, wherein the restorer utilizes the local optimization to restore the image data and further comprising: merging recovered noiseless patches or recovered high resolution patches by weighted averaging in overlap area to create the target image data.
 7. The method of claim 1, wherein the restorer utilizes the global optimization to restore the image data and further comprising: merging recovered noiseless patches or high resolution patches by weighted averaging in overlap area to create the target image data.
 8. The method of claim 1, wherein the dictionary is a combination of one or more of a prior dictionary, a self-similarity dictionary or a derived dictionary.
 9. The method of claim 8, wherein the self-similarity dictionary includes a collection of matches between patches of lower resolution image data to the initial resolution image data.
 10. The method of claim 9, wherein the matches include a sub-set of patches, wherein the sub-set of patches include only patches that are in a neighborhood of the lower resolution image data.
 11. The method of claim 9, wherein the matches include all of the patches of the lower resolution image data.
 12. The method of claim 8, wherein the derived dictionary that is derived from higher resolution image data.
 13. The method of claim 1, further comprising: high pass filtering entries in the dictionary, thereby removing entries having a frequency lower than a predetermined frequency and generating a pre-processed dictionary, wherein the pre-processed dictionary includes local features that correspond to high-frequency content.
 14. The method of claim 13, wherein the pre-processed dictionary characterizes a relation between lower-resolution patches and edges and texture content within the corresponding higher-resolution patches.
 15. An image data processor, comprising: an analyzer configured to analyse, for each of a plurality of voxels of image data, a set of entries of a dictionary, wherein an entry represents either a mapping between a lower resolution patch of voxels and a corresponding higher resolution patch of voxel, or a local neighborhood around a voxel and derives, for each of the plurality of voxels, a subspace based on the analysis, wherein the subspace is for one of the mapping or the local neighborhood; and an image restore configured to restore the image data to produce target image data which has higher image resolution or reduced image noise relative to the image data, based on the subspaces, using a least-squares approach to optimize a local or global optimization.
 16. The image data processor of claim 15, wherein the analyzer derives the subspaces by identifying patches for each voxel in the image data that are similar to a currently processed patch around the voxel, creating a data matrix with the identified patches, performing one of a PCA or weighted PCA to the matrix, and estimating a number of principle components with a largest corresponding eigenvalues to model the local patch.
 17. The image data processor of claim 15, wherein a number of similar patches with a weighted average value larger than a weighted average value of a currently processed patch is equal to a number of patches with a smaller weighted average.
 18. The image data processor of claim 15, wherein the restorer merges recovered noiseless patches or recovered high resolution patches by weighted averaging in overlap area to create the target image data.
 19. The image data processor of claim 15, wherein the dictionary is a combination of one or more of a prior dictionary, a self-similarity dictionary or a derived dictionary.
 20. The image data processor of claim 19, wherein the self-similarity dictionary includes a collection of matches between patches of lower resolution image data to their corresponding downed scaled patches, wherein the collection includes subset of patches that are in a neighborhood of the lower resolution image data.
 21. The image data processor of claim 19, wherein the self-similarity dictionary includes a collection of matches between patches of lower resolution image data to their corresponding downed scaled patches, wherein the collection includes all of the patches of the lower resolution image data.
 22. The image data processor of claim 19, wherein the derived dictionary is derived from higher resolution image data.
 23. The image data processor of claim 15, further comprising: a filter configured to high pass filter entries in the dictionary, thereby removing entries having a frequency lower than a predetermined frequency and generating a pre-processed dictionary, wherein the pre-processed dictionary includes local features that correspond to high-frequency content.
 24. The image data processor of claim 23, wherein the pre-processed dictionary characterizes a relation between lower-resolution patches and edges and texture content within the corresponding higher-resolution patches.
 25. A computer readable medium encoded with computer executable instruction, which, when executed by a processor, causes the processor to: analyze, for each of a plurality of voxels of image data, a set of entries of a dictionary, wherein an entry represents with a mapping between a lower resolution patch of voxels and a corresponding higher resolution patch of voxel, or a local neighborhood around a voxel; derive, for each of the plurality of voxels, a subspace based on the analysis, wherein the subspace is for one of the mapping or the local neighborhood; and restore the image data to produce target image data, which has higher image resolution or reduced image noise relative to the image data, based on the subspaces, using a least-squares approach to optimize a local or global optimization. 